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Page 1: ANSWERS TO ALL EXERCISES - Cengage...ANSWERS TO ALL EXERCISES - Cengage ... is ." " ." ."

ANSWERS TO ALL

EXERCISES

Page 2: ANSWERS TO ALL EXERCISES - Cengage...ANSWERS TO ALL EXERCISES - Cengage ... is ." " ." ."

266

Copyright © Houghton Mifflin Company. All rights reserved.

ANSWERS CHAPTER 1

EXERCISE 1.1

WARM-UPS A

1. 1 1021

2. 2 2340

3. 1 34

4. 378

5. -1 45

6. - 2 56

7. 1 14

8. 2 35

9. -4 25

10. -237

CLAST PRACTICE A

11. D

12. A

13. B

14. D

WARM-UPS B

15. 1 27

16. 13

17. 4 12

18. 6

19. 4 23

20. 19

21. 112

22. 213

23. -68

24. -60

CLAST PRACTICE B

25. D

26. A

27. B

28. D

EXTRA PRACTICE

29. D

30. C

31. C

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CHAPTER 1 Answers 267

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 1.2

WARM-UPS A

1. (3 × 3 × 3 × 3 × 3)(2 × 2)

2. (4 × 4 × 4)(8 × 8 × 8 × 8)

3. (2)(2)(2) + (9)(9)(9)

4. (9)(9)(9) + (3)(3)(3)

5. 63 × 63

6. 74 × 74

CLAST PRACTICE A

7. B

8. D

9. D

WARM-UPS B

10. 1

104

11. 1

103

12. (8 × 101) + (4 × 100)+

(6 × 110 ) + (7 ×

1102 ) +

(4 × 1

103 )

13. (2 × 102)+(9 × 101) +

(4 × 100) + (9 × 110 ) + (7 ×

1102 )

14. 0.11001

15. 0.20101

16. (3 × 104) + (4 × 102)

+(7 × 101) + (8 × 100)

17. (1 × 104)+(2 × 103)

(5 × 101)+(7 × 100)

CLAST PRACTICE B

18. B

19. C

20. A

21. C

22. C

EXTRA PRACTICE

23. B

24. B

25. C

26. D

27. A

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268 ANSWERS TO ALL EXERCISES

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 1.3

WARM-UPS A

1. $12,600

2. $100

3. $19

4. $36

5. 900

6. 300

7. B

8. C

9. $20,000

10. $640

11. 114 and 37

58

12. 234 and 46

CLAST PRACTICE A

13. A

14. C

15. B

16. C

17. B

18. D

WARM-UPS B

19. 5.967

20. 5.875

21. 6.969

22. 15.803

23. -27.069

24. -14.851

25. 8.626

26. 9.231

27. 59.04

28. 97.03

29. -7.29

30. -46.25

31. 291.7

32. 347

33. -6.2

34. -5.8

CLAST PRACTICE B

35. B

36. A

37. C

38. A

39. D

40. B

41. C

42. A

EXTRA PRACTICE

43. B

44. C

45. D

46. A

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CHAPTER 1 Answers 269

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 1.4

WARM-UPS A

1. 27

100

2. 2350

3. 115

4. 72

5. 0.75 6. 0.12 7. 0.45 8. 1.75 9. 1.5 10. 4.5 11. 0.18 12. 0.49 13. 0.032 14. 0.089 15. 0.0825 16. 0.0975 17. 7% 18. 1% 19. 36% 20. 85% 21. 13.9% 22. 38.4% 23. 312% 24. 506% 25. 325% 26. 750% 27. 18.2% 28. 21.4% 29. 2.8% 30. 9.5% 31. 15%

32. 20%

33. 87.5%

34. 50%

35. 37.5%

36. 24%

37. 39

100

38. 3

25

39. 29

200

40. 2380

CLAST PRACTICE A 41. A 42. D 43. C 44. A 45. D 46. A 47. < 48. > 49. > 50. < 51. < 52. > 53. > 54. < 55. = 56. = 57. > 58. < 59. > 60. <

CLAST PRACTICE B 61. C 62. B 63. A 64. B 65. C 66. B 67. C 68. B 69. A 70. B 71. C 72. B WARM-UPS C

73. - 2

243

74. - 4

243

75. 9 76. -20

77. 1

51

78. 1

60

79. 1

12

80. 16

CLAST PRACTICE C 81. D 82. A EXTRA PRACTICE 83. C 84. B 85. A 86. D

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270 ANSWERS TO ALL EXERCISES

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 1.5

WARM-UPS A 1. 60% 2. 60% 3. 25% 4. 20% 5. 40% 6. 60% 7. 104 8. 50 9. 48 10. 24 CLAST PRACTICE A 11. C 12. B 13. B 14. C WARM-UPS B 15. 14 16. 25.2 17. 102 18. 133 19. 112.5 20. 128.8 21. 49.35 22. 8.1 23. 16.6 24. 150.75 25. 20% 26. 50% 27. 400%

28. 150% 29. 30 30. 60 31. 10 32. 50 33. 2 34. 100 CLAST PRACTICE B 35. C 36. B 37. D 38. D 39. C 40. B WARM-UPS C 41. $2500 42. $24 43. $12 44. $5; $20 45. $9.80 46. $32 47. $48 48. $58 CLAST PRACTICE C 49. B 50. C EXTRA PRACTICE 51. A 52. B 53. D 54. B

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CHAPTER 1 Answers 271

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 1.6

WARM-UPS A

1. $730

2. $20.60

3. $1

4. $0.96

5. 43

6. 13

7. $72

8. $440

9. 13

10. 15

CLAST PRACTICE A

11. D

12. A

13. C

14. B

15. D

WARM-UPS B

16. 45

17. 9

18. 2 (6 and 12)

19. 3 (4, 8 and 16)

CLAST PRACTICE B

20. D

21. A

EXTRA PRACTICE

22. B

23. D

24. C

25. D

26. B

27. C

28. B

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272

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ANSWERS CHAPTER 2 EXERCISE 2.1

WARM-UPS A

1. 14π - 5

2. 14π - 3

3. 7π - 7

4. - 5π − 2

5. 5 2

6. 7 3

7. 7

8. 2 10

9. 7 5

10. 11 3

11. 5 6

12. 5 14

13. 4 5

5

14. 7 6

6

15. 3 2

4

16. 5 3

9

17. 6

6

18. 13

CLAST PRACTICE A

19. A

20. B

21. D

22. C

23. A

24. C

25. D

26. B

WARM-UPS B

27. 1,705,000

28. 21,600

29. 0.04185

30. 0.001584

31. 2 ∞ 10-8

32. 2 ∞ 10-5

33. 4.2 ∞ 10-6

34. 2 ∞ 10-9

CLAST PRACTICE B

35. A

36. D

37. B

38. A

WARM-UPS C

39. - 3613

40. - 2423

41. - 9910

42. - 10

43. 6t2 - 3t

44. 8t2 + 5t

45. 8t2 - 13t

46. 14t2 + 13t

CLAST PRACTICE C

47. A

48. D

49. A

50. C

EXTRA PRACTICE

51. B

52. C

53. A

54. B

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CHAPTER 2 Answers 273

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 2.2

WARM-UPS A

1. 20(5 + 7)

2. a[(-4) + (-6)]

3. a[5 + (-3)]

4. -c(7 + 9)

5. (5 + 3) + 2

6. (9 + 3) + x

7. 3 × a + 3 × b

8. 7 × x + 7 × z

9. (3a2a5)b4

10. (-5x3x7)y2

CLAST PRACTICE A

11. B

12. D

13. B

14. A

15. D

16. C

17. A

WARM-UPS B

18. x - 7 = 2

19. x - 9 = 4

20. x - 17 = 20

21. 23x - 6 = 27

22. 12a - 90 = 7

23. 13a - 56 = 3

24. 3x > -3

25. 5x > 1

26. 7x < 5

27. 9x < 3

28. 3x > 6

29. 4x > 6

30. x > -35

31. x > - 24

CLAST PRACTICE B

32. D

33. A

34. A

35. D

EXTRA PRACTICE

36. B

37. A

38. A

39. C

40. D

41. B

42. A

43. C

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274 ANSWERS TO ALL EXERCISES

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 2.3 WARM-UPS A 1. x = 14 2. x = - 5 3. x = -9 4. x = - 10 5. x = 3 6. x = - 3

7. y = 83 or 2

23

8. y = 52 or 2

12

9. y = 132 or 6

12

10. y = 134 or 3

14

11. y = 3

12. y = 76 or 1

16

13. z = 28 14. z = -12 15. b = 6 16. b = 3

17. a = 5913 or 4

713

18. a = 269 or 2

89

19. a = 229 or 2

49

20. a = 118 or 1

38

CLAST PRACTICE A 21. B 22. C 23. C 24. A 25. A 26. C WARM-UPS B 27. x < 4 28. x > 2 29. x > -3 30. x < -2 31. b ≤ -25 32. b ε -24 33. x ≤ 2 34. x ε 5 CLAST PRACTICE B 35. B

36. B 37. C 38. D 39. A 40. B WARM-UPS C 41. No 42. Yes

43. Yes

44 Yes 45. No 46. Yes 47. Yes 48. Yes 49. Yes 50. No CLAST PRACTICE C 51. A 52. D

53. D

54. C

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CHAPTER 2 Answers 275

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 2.4 WARM-UPS A 1. a = 196 2. b = 169 3. c = 81 4. d = 6 5. W = 160 lbs 6. W = 100 lbs 7. H = 14 years

8. t = 4 hours CLAST PRACTICE A 9. A 10. A 11. B 12. D 13. C 14. A 15. A

WARM-UPS B 16. 11 17. 15 18. -4 19. 14 CLAST PRACTICE B 20. D 21. A 22. B 23. A 24. C 25. A

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276 ANSWERS TO ALL EXERCISES

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 2.5 WARM-UPS A

1. 2x + 3, x + 1 2. 2x + 1, x + 3 3. 4y - 3, y - 2 4. 3y - 2, y - 5 5. 3y + 1, y - 2 6. 4y - 3, 3y + 2 7. 5x + 1, x + 2 8. 5x + 3, x + 1 9. 3x + 1, x - 2 10. 5x + 4, x - 2 11. x + 1, x - 1 12. x + 6, x - 6 13. 3x + 2, 3x - 2

14. 4x + 5, 4x - 5

CLAST PRACTICE A 15. A 16. D 17. B

18. C

WARM-UPS B

19. x = - 12 , x = - 3

20. x = - 32 , x = -1

21. x = 0

22. x = 32 , x = -

43

23. x = - 13 , x = 2

24. x = 34 , x = -

23

25. y = 23 , y = 5

26. y = - 13 , y = 1

27. x = - 32 , x= - 2

28. x = -7 ± 97

4

29. x = 57 , x = 1

30. x = -8 ± 2 6

5

CLAST PRACTICE B 31. A 32. A 33. A 34. B 35. C EXTRA PRACTICE 36. D 37. A

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CHAPTER 2 Answers 277

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 2.6 WARM-UPS A 1. {(3, 1)} 2. {(-1, 2)} 3. {(-2, -3)} 4. {(3, -3)} 5. The empty set 6. The empty set 7. {(-3, -3)}

8. {(x, y) | y = 34 x -

14 }

9. {(x, y) | y = - 32 x + 6}

10. The empty set CLAST PRACTICE A 11. D 12. B 13. A 14. D 15. C WARM-UPS B

5–5

5

–5

x + y = 3x + y = 316.

5–5

5

–5

x - y = - 3

17.

5–5

5

–5

2x + y = 42x + y = 418.

5–5

5

–5

x - 2y = 4x - 2y = 4

19.

5–5

5

–5

x = 3

20.

5–5

5

–5y = -3y = -3

21.

5–5

5

–5

x = -4x = -4

22.

5–5

5

–5

y = 4y = 423.

24. x ≥ -4 25. y < -4 26. 4x + y ≥ 4 27. x - 2y > -4 28. x ≥ 1 and y ≥ 2 29. 2x + y ≤ 4 30. 4x - 3y > -12 x ≤ 0 and y ≥ 0 31. -3x + y > -3 CLAST PRACTICE B

32. D

33. B

34. D

35. D

36. C

37. D

38. B

39. C

40. A

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278 ANSWERS TO ALL EXERCISES

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 2.7 WARM-UPS A

1. 75 =

t30

2. L11 =

42

3. 68 =

39F or

34 =

39F

CLAST PRACTICE A 4. C 5. D 6. D WARM-UPS B

7. 112 lb per sq. in.

8. 900 lb per sq. in. CLAST PRACTICE B 9. D

10. D

WARM-UPS C 11. x - (5x + 2) = 9 12. x - (4x + 6) = 5 13. x + 17 = 36 14. 5x = x - 2 15. x - 7 = 8 x

16. x3 = x + 2

17. n + (n + 1) + (n + 2) =

(n + 1)2 18. (n + 2)2 > n(n + 1) 19. 10x + (x - 4)=21(x - 4) 20. x2 + 2x = x + 7 CLAST PRACTICE C 21. B 22. A 23. C 24. D 25. D

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CHAPTER 3 Answers 279

Copyright © Houghton Mifflin Company. All rights reserved.

ANSWERS CHAPTER 3 EXERCISE 3.1

WARM-UPS A 1. 3 in.

2. 212 in.

CLAST PRACTICE A 3. D WARM-UPS B 4. 900 m 5. 0.900 km 6. 125 ft

7. 4123 yd

8. 16π cm 9. 10π in. 10. 100π sq. m 11. 36π sq. ft 12. 80 sq. mm 13. 8 sq. yd 14. 6 sq. km 15. 7 sq. ft 16. 412 sq. cm 17. 352 sq. in.

18. 384 cu. in.

19. 6000 cu. mm 20. 576π cu. in. 21. 300π cu. cm

22. 90π cu. ft

23. 43 π cu. ft

24. 323 π cu. yd

25. 195 cl 26. 390 cl CLAST PRACTICE B 27. C 28. C 29. B 30. C 31. D 32. B 33. A 34. A 35. C 36. D 37. C

38. B WARM-UPS C 39. Linear 40. Linear 41. Square 42. Square 43. Cubic (or gallons or liters) 44. Cubic (or gallons or liters)

CLAST PRACTICE C 45. B 46. C 47. A 48. B 49. C 50. C EXTRA PRACTICE 51. B 52. A

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280 ANSWERS TO ALL EXERCISES

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 3.2 WARM-UPS A 1. $972

2. 123

3. $270

4. 889

5. 0.8 liter 6. $360 7. $2160 8. 30π 9. 60 ft 10. 50 mi 11. 97 ≈ 9.8 ft 12. $900 CLAST PRACTICE A 13. C 14. D 15. B 16. C

17. C

WARM-UPS B

18. 25 3

2 sq. units

19. A = 3bh

20. A = rh + 12 πr2

21. P = 2πs

22. A = s2 + 12 πs2

CLAST PRACTICE B 23. A 24. C 25. C 26. C 27. A 28. A 29. D 30. B 31. D

EXTRA PRACTICE 32. C 33. C 34. D 35. C

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CHAPTER 3 Answers 281

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 3.3 WARM-UPS A 1. ∠ 1 and ∠ 6; ∠ 3 and ∠ 4 ∠ 1 and ∠ 3; ∠ 4 and ∠ 6 2. ∠ 2 and ∠ 5 3. ∠ 2 and ∠ 5; ∠ 3 and ∠ 6; ∠ 1 and ∠ 4. 4. ∠ 2 and ∠ 5 5. ∠ 1, ∠ 3, ∠ 4, ∠ 6 6. No 7. 60o 8. 30o 9. 90o 10. y = 30o, z = 75o 11. Acute, equilateral 12. Obtuse, scalene 13. Right, scalene 14. Acute, isosceles 15. Square 16. Trapezoid

CLAST PRACTICE A 17. D 18. C 19. D 20. B 21. C

WARM-UPS B 22. 115o 23. 65o 24. 65o 25. 70o 26. 70o 27. 40o 28. 45o 29. 45o 30. 90o 31. 90o 32. 75o 33. 75o

34. 30o 35. B

CLAST PRACTICE B 36. B 37. D 38. B 39. C 40. D WARM-UPS C

41. x = 513 , y = 6

23

42. 12.5 43. 14

44. 313

45. 113

46. 4 CLAST PRACTICE C 47. B 48. A 49. A 50. B EXTRA PRACTICE 51. C 52. B

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282

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ANSWERS CHAPTER 4 EXERCISE 4.1

WARM-UPS A 1. Not everybody in the

city has an equal chance.

2. Not the target popula-

tion.

CLAST PRACTICE A

3. C

4. A

WARM-UPS B

5. 42%

6. 68%

7. 45-54

8. 55+

9. 55+

10. 40%; 45-54

11. Dept. Stores

12. Specialty Stores

13. Dept. Stores

14. Specialty Stores

15. 37%

16. 23%

17. 40%

18. 4%

CLAST PRACTICE B 19. Never washed 20. D 21. B 22. C 23. C

WARM-UPS C

24. Increased

25. Stabilized

26. Age Under 14

27. Age 65+

28. 26 mpg

29. 23 mpg 30. As the speed in-

creases, the mpg decreases.

CLAST PRACTICE C

31. C

32. B

33. D

EXTRA PRACTICE

34. B

35. A

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CHAPTER 4 Answers 283

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 4.2 WARM-UPS A 1. 8 2. 16 3. 6 CLAST PRACTICE A 4. C 5. D 6. A 7. B 8. C WARM-UPS B

9. median < mean

10. mode < mean

11. mode < median

12. 5 years

CLAST PRACTICE B

13. C

14. D

15. D

16. B

WARM-UPS C 17. 2 18. 2 19. 2.57 20. 2 21. 0 22. 1.70 23. O.56 24. 14 25. 26 26. 29 27. $34,999 28. $10,000 CLAST PRACTICE C 29. D 30. C 31. B 32. D 33. C 34. A 35. D

EXTRA PRACTICE 36. B 37. D 38. C 39. B 40. A 41. D 42. C

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284 ANSWERS TO ALL EXERCISES

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 4.3

WARM-UPS A 1. 120 2. 720 3. 24 4. 15

5. 32

6. 10

7. 10

8. 60

CLAST PRACTICE A

9. D

10. C

11. B

12. C

13. D

14. A

15. C

WARM-UPS B

16. 15

17. 45

18. 35

19. 25

20. 110

21. 81100

22. 145

23. 0.06 or 350

24. 0.20 or 15

25. 0.6 or 35

CLAST PRACTICE B

26. A

27. B

28. C

29. C

30. B

31. C

32. D

33. C

34. B

WARM-UPS C

35. 0.20 or 15

36. 0.90 or 910

37. 0.30 or 310

38. 60% or 35

39. 10% or 110

40. 37

41. 23

42. 55% or 1120

43. 35

44. 45% or 920

45. 80 CLAST PRACTICE C

46. C

47. A

48. D

49. B

50. C

51. A

EXTRA PRACTICE

52. B

53. B

54. A

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CHAPTER 5 Answers 285

Copyright © Houghton Mifflin Company. All rights reserved.

ANSWERS CHAPTER 5 EXERCISE 5.1

WARM-UPS A 1. It is snowing or the sun it not out. 2. It is not warm and the

air conditioner is not broken.

3. Bill will not study Math

and he will pass the test.

4. It does not rain and we

will not go to the beach. 5. The sun is out and the

temperature will not rise.

6. Some athletes are not in

good shape. 7. No athletes are in good

shape. 8. Some athletes are in

good shape. 9. All athletes are in good

shape. CLAST PRACTICE A 10. D 11. C 12. D 13. B

WARM-UPS B 14. Today is not Monday

or I will study. I will study or today is

not Monday. If I will not study then

today is not Monday. 15. Joe did not take Math

or Joe did not fail it. 16. Wendy is not

intelligent and Wendy is not aloof.

17. Pat is a not boy or

Jackie is a not boy. CLAST PRACTICE B 18. B 19. C 20. C 21. A

WARM-UPS C 22. "Not all are p" is

equivalent to "Some are not p."

23. "Some are p" is

equivalent to "It is not true that none are p."

24. "Not all are p" is

equivalent to "Some are not p."

25. "All are not p" is

equivalent to "None are p."

CLAST PRACTICE C 26. A 27. C 28. A 29. D 30. D 31. A EXTRA PRACTICE 32. B 33. A 34. C

35. D

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286 ANSWERS TO ALL EXERCISES

Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 5.2

WARM-UPS A 1. Every element of

set A is also an element of set B.

2. There is no

element that is in both A and C.

3. There is no

element that is in both C and B.

4. Every element of

set A is also an element of set U.

5. No. 6. Yes. CLAST PRACTICE A 7. B 8. A 9. A 10. D

WARM-UPS B 11. No supervisors are

lovable. 12. No politicians are

reliable. 13. Some employees will

not be promoted. 14. Some students are

snobs. 15. Ms. A 16. Mr. S CLAST PRACTICE B 17. A 18. C 19. D 20. B 21. A

WARM-UPS C 22. You get a good job. 23. I will go to college. 24. If you are rich, then

you visit France. CLAST PRACTICE C 25. C 26. C 27. D 28. B

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CHAPTER 5 Answers 287

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EXERCISE 5.3

WARM-UPS A 1. The car will start. 2. We do not want to

save money. 3. The car will not

start. 4. If you use the

right bait, you will have a nice dinner.

5. All dogs have

legs. 6. Some Math

students won't pass the course.

CLAST PRACTICE A 7. A 8. B 9. B 10. D

WARM-UPS B 11. Valid 12. Invalid 13. Valid 14. Valid 15. Valid 16. Valid CLAST PRACTICE B 17. B 18. C 19. A 20. B EXTRA PRACTICE 21. C 22. B 23. D 24. B 25. A